@fify-- I think the main difference between the two is the cause. If you eat something or get bitten by an insect and then see a rash, it's probably hives. And someone who has hives usually also has other symptoms. I'm allergic to strawberries and I also get swelling and itchy skin in addition to hives from it.
If the rash appears out of nowhere and doesn't go away, it's probably not an allergic reaction.